Vertex-labeling algorithms for the Hilbert spacefilling curve

We describe a method, based on vertex-labeling, to generate algorithms for manipulating the Hilbert space lling curve in the following ways: 1. Computing the image of a point in R. 2. Computing a pre-image of a point in R. 3. Drawing a nite approximation of the curve. 4. Finding neighbor cells in a decomposition ordered according to the curve. Our method is straightforward and exible, resulting in short, intuitive procedures that are as e cient as specialized procedures found in the literature. Moreover, the same method can be applied to many other space lling curves. We demonstrate vertex-labeling algorithms for the Sierpinski and Peano space lling curves, and variations.